Prolonged Learning and Hasty Stopping: the Wald Problem with Ambiguity

TL;DR

This paper examines how ambiguity-averse decision makers gather information over time, revealing complex behaviors like excessive experimentation under moderate uncertainty and premature stopping under high uncertainty, with non-monotonic stopping rules.

Contribution

It introduces a model of sequential information acquisition under ambiguity, highlighting novel dynamic behaviors such as randomized stopping and non-monotonic stopping rules.

Findings

Ambiguity leads to excessive experimentation at moderate uncertainty.

High uncertainty causes premature, sometimes randomized, stopping.

Stopping rules are non-monotonic in beliefs.

Abstract

This paper studies sequential information acquisition by an ambiguity-averse decision maker (DM), who decides how long to collect information before taking an irreversible action. The agent optimizes against the worst-case belief and updates prior by prior. We show that the consideration of ambiguity gives rise to rich dynamics: compared to the Bayesian DM, the DM here tends to experiment excessively when facing modest uncertainty and, to counteract it, may stop experimenting prematurely when facing high uncertainty. In the latter case, the DM's stopping rule is non-monotonic in beliefs and features randomized stopping.